4(x-8)x=5(x-7)+3

Solution for 4(x-8)x=5(x-7)+3 equation:

4(x-8)x=5(x-7)+3

We move all terms to the left:

4(x-8)x-(5(x-7)+3)=0

We multiply parentheses

4x^2-32x-(5(x-7)+3)=0


We calculate terms in parentheses: -(5(x-7)+3), so:

5(x-7)+3

We multiply parentheses

5x-35+3

We add all the numbers together, and all the variables

5x-32

Back to the equation:

-(5x-32)


We get rid of parentheses

4x^2-32x-5x+32=0

We add all the numbers together, and all the variables

4x^2-37x+32=0

a = 4; b = -37; c = +32;
Δ = b2-4ac
Δ = -372-4·4·32
Δ = 857
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-37)-\sqrt{857}}{2*4}=\frac{37-\sqrt{857}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37)+\sqrt{857}}{2*4}=\frac{37+\sqrt{857}}{8}
$